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Simplify completely. `2/(3-2i)`

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connorcolin3 | Valedictorian

Posted May 9, 2013 at 11:57 PM via web

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Simplify completely.

`2/(3-2i)`

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mjripalda | High School Teacher | (Level 3) Educator

Posted May 10, 2013 at 2:18 AM (Answer #2)

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`2/(3-2i)`

To simplify, multiply the top and bottom by the conjugate of the denominator.

`=2/(3-2i)*(3+2i)/(3+2i)`

`=(2(3+2i))/(9-4i^2)`

Since i^2=-1, then:

`=(2(3+2i))/(9-4(-1))`

`=(2(3+2i))/(9+4)`

`=(2(3+2i))/13`

`=(6+4i)/13`

`=6/13+4/13i`

Hence, `2/(3-2i)=6/13 + 4/13i` .

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